On the integrable perturbations of the Camassa-Holm equation

We present an investigation of the nonlinear partial differential equations (PDE) which are asymptotically representable as a linear combination of the equations from the Camassa-Holm hierarchy. For this purpose we use the infinitesimal transformations of dependent and independent variables of the original PDE. This approach is helpful for the analysis of the systems of the PDE which can be asymptotically represented as the evolution equations of polynomial structure. © 2000 American Institute of Physics.

Tachyon condensation in superstring field theory

It has been conjectured that at the stationary point of the tachyon potential for the D-brane-anti-D-brane pair or for the non-BPS D-brane of superstring theories, the negative energy density cancels the brane tensions. We study this conjecture using a Wess-Zumino-Witten-like open superstring field theory free of contact term divergences and recently shown to give 60% of the vacuum energy by condensation of the tachyon field alone. While the action is non-polynomial, the multiscalar tachyon potential to any fixed level involves only a finite number of interactions. We compute this potential to level three, obtaining 85% of the expected vacuum energy, a result consistent with convergence that can also be viewed as a successful test of the string field theory. The resulting effective tachyon potential is bounded below and has two degenerate global minima. We calculate the energy density of the kink solution interpolating between these minima finding good agreement with the tension of the D-brane of one lower dimension. © 2000 Elsevier Science B.V.

Variational studies and replica symmetry breaking in the generalization problem of the binary perceptron

We analyze the average performance of a general class of learning algorithms for the nondeterministic polynomial time complete problem of rule extraction by a binary perceptron. The examples are generated by a rule implemented by a teacher network of similar architecture. A variational approach is used in trying to identify the potential energy that leads to the largest generalization in the thermodynamic limit. We restrict our search to algorithms that always satisfy the binary constraints. A replica symmetric ansatz leads to a learning algorithm which presents a phase transition in violation of an information theoretical bound. Stability analysis shows that this is due to a failure of the replica symmetric ansatz and the first step of replica symmetry breaking (RSB) is studied. The variational method does not determine a unique potential but it allows construction of a class with a unique minimum within each first order valley. Members of this class improve on the performance of Gibbs algorithm but fail to reach the Bayesian limit in the low generalization phase. They even fail to reach the performance of the best binary, an optimal clipping of the barycenter of version space. We find a trade-off between a good low performance and early onset of perfect generalization. Although the RSB may be locally stable we discuss the possibility that it fails to be the correct saddle point globally. ©2000 The American Physical Society.

Lamé differential equations and electrostatics

The problem of existence and uniqueness of polynomial solutions of the Lamé differential equation A(x)y″ + 2B(x)y′ + C(x)y = 0, where A(x),B(x) and C(x) are polynomials of degree p + 1,p and p - 1, is under discussion. We concentrate on the case when A(x) has only real zeros aj and, in contrast to a classical result of Heine and Stieltjes which concerns the case of positive coefficients rj in the partial fraction decomposition B(x)/A(x) = ∑j p=0 rj/(x - aj), we allow the presence of both positive and negative coefficients rj. The corresponding electrostatic interpretation of the zeros of the solution y(x) as points of equilibrium in an electrostatic field generated by charges rj at aj is given. As an application we prove that the zeros of the Gegenbauer-Laurent polynomials are the points of unique equilibrium in a field generated by two positive and two negative charges. © 2000 American Mathematical Society.

PI Stabilization of a Class of Time Delay Systems

In this paper we use the Hermite-Biehler theorem to establish results for the design of proportional plus integral (PI) controllers for a class of time delay systems. We extend results of the polynomial case to quasipolynomials using the property of interlacing in high frequencies of the class of time delay systems considered. A signature for the quasipolynomials in this class is derived and used in the proposed approach which yields the complete set of the stabilizing PI controllers.

Orthogonal polynomials associated with related measures and Sobolev orthogonal polynomials

Connection between two sequences of orthogonal polynomials, where the associated measures are related to each other by a first degree polynomial multiplication (or division), are looked at. The results are applied to obtain information regarding Sobolev orthogonal polynomials associated with certain pairs of measures.

Behavioural Analysis of a Nonlinear Mechanical System Using Transient Trajectories

This work aims at a better comprehension of the features of the solution surface of a dynamical system presenting a numerical procedure based on transient trajectories. For a given set of initial conditions an analysis is made, similar to that of a return map, looking for the new configuration of this set in the first Poincaré sections. The mentioned set of I.C. will result in a curve that can be fitted by a polynomial, i.e. an analytical expression that will be called initial function in the undamped case and transient function in the damped situation. Thus, it is possible to identify using analytical methods the main stable regions of the phase portrait without a long computational time, making easier a global comprehension of the nonlinear dynamics and the corresponding stability analysis of its solutions. This strategy allows foreseeing the dynamic behavior of the system close to the region of fundamental resonance, providing a better visualization of the structure of its phase portrait. The application chosen to present this methodology is a mechanical pendulum driven through a crankshaft that moves horizontally its suspension point.

Estimates of covariance functions for growth of Nelore cattle applying a parametric correlation structure to model within-animal correlations

A total of 20,065 weights recorded on 3016 Nelore animals were used to estimate covariance functions for growth from birth to 630 days of age, assuming a parametric correlation structure to model within-animal correlations. The model of analysis included fixed effects of contemporary groups and age of dam as quadratic covariable. Mean trends were taken into account by a cubic regression on orthogonal polynomials of animal age. Genetic effects of the animal and its dam and maternal permanent environmental effects were modelled by random regressions on Legendre polynomials of age at recording. Changes in direct permanent environmental effect variances were modelled by a polynomial variance function, together with a parametric correlation function to account for correlations between ages. Stationary and nonstationary models were used to model within-animal correlations between different ages. Residual variances were considered homogeneous or heterogeneous, with changes modelled by a step or polynomial function of age at recording. Based on Bayesian information criterion, a model with a cubic variance function combined with a nonstationary correlation function for permanent environmental effects, with 49 parameters to be estimated, fitted best. Modelling within-animal correlations through a parametric correlation structure can describe the variation pattern adequately. Moreover, the number of parameters to be estimated can be decreased substantially compared to a model fitting random regression on Legendre polynomial of age. © 2004 Elsevier B.V. All rights reserved.

Análise da transformação do uso da terra, vegetação e impactos ambientais por meio de sensoriamento remoto e geoprocessamento

The mapping of the land use, vegetation and environmental impacts using remote sensing and geoprocessing allows detection, spatial representation and quantifying all alterations due to the human action in the nature, contributing to the monitoring and planning of those activities that cause damages to the environment. The aim of this research is analyze the transformation ocurred with the land use and vegetation in order to detect environmental impacts during the period from 1962 to 1995, considering a test area in the district of Assistência and surroundings, in the Rio Claro (SP) region. In order to archieve such aim the authors used boolean operations available in the Geographical Information System (GIS) - Idrisi. The maps were obtained through the ordinary (conventional) interpretation of aerial photos, later digitized in the software CAD Overlay and georeferenced in AutoCAD Map. It's observed that operations such as crossing digitized maps of one specific area in two differents dates, using GIS, produce overall results that might point out expansion or retraction's trends of the mapped classes, as well as quantify the intensity of the phenomena.

Carta de Aptidão para a implantação de rodovias e avaliação de alternativas de traçado com uso de geotecnologias

This study discuss the use of the geotechnologies to aid the planners on the terrain aptness definition for highways implantation and on the different trace evaluation to the extention of the Governador Carvalho Pinto highway, between Taubaté-SP and Aparecida do Norte-SP. Fratures on the area were mapping using Landsat ETM+, band Pan. In order to elaborate the phisical aptness chart for highway implantation was used the Analitical Hierarchy Process (AHP) operation, in on geographical information system (GIS). Using GIS were realized a ponderate middle with the soils, rocks, relief, slope, fractures and land use/cover maps. Using this physical aptness chart and joinning it with urban and restrict areas (that was inserted by the Boolean operation), were obtained a viability chart for highway implantation. Based on it were proposed three aleatory traces for the Carvalho Pinto highway. This traces were evaluated with the cross tabulation operation. The integration of the restrict areas, land use and phisical aptness in digital media can offer for the planners the cartography of the viability for the highway implantation. The evaliation of these three traces, based on the viability chart, can subsidyse the decision by the planners.

Um modelo para orientação de imagens orbitais baseado em feições retas

The aim of this paper is to present a model for orientation of pushbroom sensors that allows estimating the polynomial coefficients describing the trajectory of the platform, using linear features as ground control. Considering that pushbroom image acquisition is not instantaneous, six EOP (Exterior Orientation Parameters) for each scanned line must be estimated. The sensor position and attitude parameters are modeled with a time dependent polynomial. The relationship between object and image space is established through a mathematical model based on the equivalence between the vector normal to the projection plane in the image space and to the vector normal to the rotated projection plane in the object space. The equivalence property between planes was adapted to consider the pushbroom geometry. Some experiments with simulated data corresponding to CBERS scene (China-Brazil Earth Resource Satellite) were accomplished in order to test the developed model using straight lines. Moreover, experiments with points ground with the model based on collinearity equations adapted to the pushbroom geometry were also accomplished. The obtained results showed that the proposed model can be used to estimate the EOP of pushbroom images with suitable accuracy.

Identification of structural parameters for active vibration control

The study of algorithms for active vibration control in flexible structures became an area of enormous interest for some researchers due to the innumerable requirements for better performance in mechanical systems, as for instance, aircrafts and aerospace structures. Intelligent systems, constituted for a base structure with sensors and actuators connected, are capable to guarantee the demanded conditions, through the application of diverse types of controllers. For the project of active controllers it is necessary, in general, to know a mathematical model that enable the representation in the space of states, preferential in modal coordinates to permit the truncation of the system and reduction in the order of the controllers. For practical applications of engineering, some mathematical models based in discrete-time systems cannot represent the physical problem, therefore, techniques of identification of system parameters must be used. The techniques of identification of parameters determine the unknown values through the manipulation of the input (disturbance) and output (response) signals of the system. Recently, some methods have been proposed to solve identification problems although, none of them can be considered as being universally appropriate to all the situations. This paper is addressed to an application of linear quadratic regulator controller in a structure where the damping, stiffness and mass matrices were identified through Chebyshev's polynomial functions.

Freezing point and thermal conductivity of tropical fruit pulps: Mango and papaya

The freezing point depression of mango and papaya pulps was measured by using a simple apparatus, consisting of two major sections: a freezing vessel and a data acquisition system. The thermal conductivity of both pulps as a function of frozen water fraction and temperature was also investigated by using a coaxial dual-cylinder apparatus. Thermal conductivity above the initial freezing point was well fitted by polynomial equations. Below the freezing point, the thermal conductivity was strongly affected by both the frozen water fraction and temperature. Simple equations in terms of frozen water fraction and temperature could be fitted to the experimental data of freezing point depression and thermal conductivity.

Qualidade fisiológica de sementes de Sebastiania commersoniana (Baill.) Smith & Downs (branquilho - Euphorbiaceae) durante o armazenamento

This paper aims to evaluate the physiological quality of Sebastiania commersoniana seeds stored in cloth bag, plastic bag and glass container and kept in two conditions: laboratory workbench and cold chamber (4 ± 2°C e 80% relative humidity - RH) for 531 days. Periodically, samples were taken in order to determine the moisture content and to perform germination tests. The experimental design was completely randomized, in factorial scheme of 3 × 2 (wrappings × conditions), for each period of storage evaluated (0, 158, 271, 389 and 531 days of storage). Supplementary, a polynomial regression was adjusted in order to describe the physiological quality of the seeds for the different conditions during the experimental period. The results lead to the following considerations: a) storage under variable temperature and air humidity (laboratory workbench) can be used for periods of over five and a half months, with the seeds stored in cloth bag, plastic bag or glass container; b) the physiological quality of the seeds was not hardly altered when stored in cold chamber in cloth bag, plastic bag and glass container for over 18 months.

Branch and bound algorithm for transmission network expansion planning using DC model

This paper presents an algorithm to solve the network transmission system expansion planning problem using the DC model which is a mixed non-linear integer programming problem. The major feature of this work is the use of a Branch-and-Bound (B&B) algorithm to directly solve mixed non-linear integer problems. An efficient interior point method is used to solve the non-linear programming problem at each node of the B&B tree. Tests with several known systems are presented to illustrate the performance of the proposed method. ©2007 IEEE.